Augmented regression models using neurochaos learning

Abstract

This study presents novel Augmented Regression Models using Neurochaos Learning (NL), where Tracemean features derived from the Neurochaos Learning framework are integrated with traditional regression algorithms - Linear Regression, Ridge Regression, Lasso Regression, and Support Vector Regression (SVR). Regression analysis is one of the most fundamental tools in machine learning and data science, yet improving its robustness and accuracy in noisy, real-world settings remains a persistent challenge; this motivates the incorporation of chaos-inspired features. Our approach was evaluated using ten diverse real-world datasets and a synthetically generated noisy dataset of the form $y=mx+c+ϵ$ with various levels of additive Gaussian noise. Results show that incorporating the Tracemean feature (mean of the chaotic neural traces of the neurons in the NL architecture) significantly enhances regression performance, particularly in Augmented Lasso Regression and Augmented SVR, where six out of ten real-life datasets exhibited improved predictive accuracy. Among the models, Augmented Chaotic Ridge Regression achieved the highest average performance ($R^2$) boost (11.35%). Additionally, experiments on the simulated noisy dataset demonstrated that the Mean Squared Error (MSE) of the augmented models consistently decreased and converged towards the Minimum Mean Squared Error (MMSE) as the sample size increased with various levels of additive Gaussian noise. This work demonstrates the potential of chaos-inspired features in regression tasks, offering a pathway to more accurate, robust and computationally efficient prediction models.